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The Evolution of Dynamics: Vibration Theory from 1687 to 1742

  • John T. Cannon
  • Sigalia Dostrovsky

Part of the Studies in the History of Mathematics and Physical Sciences book series (HISTORY, volume 6)

Table of contents

  1. Front Matter
    Pages i-ix
  2. John T. Cannon, Sigalia Dostrovsky
    Pages 1-8
  3. John T. Cannon, Sigalia Dostrovsky
    Pages 9-14
  4. John T. Cannon, Sigalia Dostrovsky
    Pages 15-22
  5. John T. Cannon, Sigalia Dostrovsky
    Pages 23-27
  6. John T. Cannon, Sigalia Dostrovsky
    Pages 28-32
  7. John T. Cannon, Sigalia Dostrovsky
    Pages 33-36
  8. John T. Cannon, Sigalia Dostrovsky
    Pages 37-46
  9. John T. Cannon, Sigalia Dostrovsky
    Pages 47-52
  10. John T. Cannon, Sigalia Dostrovsky
    Pages 53-69
  11. John T. Cannon, Sigalia Dostrovsky
    Pages 70-76
  12. John T. Cannon, Sigalia Dostrovsky
    Pages 77-82
  13. John T. Cannon, Sigalia Dostrovsky
    Pages 83-92
  14. John T. Cannon, Sigalia Dostrovsky
    Pages 93-103
  15. John T. Cannon, Sigalia Dostrovsky
    Pages 104-109
  16. John T. Cannon, Sigalia Dostrovsky
    Pages 110-122
  17. Back Matter
    Pages 123-185

About this book

Introduction

In this study we are concerned with Vibration Theory and the Problem of Dynamics during the half century that followed the publication of Newton's Principia. The relationship that existed between these subject!! is obscured in retrospection for it is now almost impossible not to view (linear) Vibration Theory as linearized Dynamics. But during the half century in question a theory of Dynamics did not exist; while Vibration Theory comprised a good deal of acoustical information, posed definite problems and obtained specific results. In fact, it was through problems posed by Vibration Theory that a general theory of Dynamics was motivated and discovered. Believing that the emergence of Dynamics is a critically important link in the history of mathematical science, we present this study with the primary goal of providing a guide to the relevant works in the aforemen­ tioned period. We try above all to make the contents of the works readily accessible and we try to make clear the historical connections among many of the pertinent ideas, especially those pertaining to Dynamics in many degrees of freedom. But along the way we discuss other ideas on emerging subjects such as Calculus, Linear Analysis, Differential Equations, Special Functions, and Elasticity Theory, with which Vibration Theory is deeply interwound. Many of these ideas are elementary but they appear in a surprising context: For example the eigenvalue problem does not arise in the context of special solutions to linear problems-it appears as a condition for isochronous vibrations.

Keywords

Degrees of freedom Evolution Finite Schwingung calculus equation function theorem

Authors and affiliations

  • John T. Cannon
    • 1
  • Sigalia Dostrovsky
    • 1
  1. 1.Yellow SpringsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9461-7
  • Copyright Information Springer-Verlag New York 1981
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9463-1
  • Online ISBN 978-1-4613-9461-7
  • Series Print ISSN 0172-570X
  • Buy this book on publisher's site